Robust Output Regulation of Euler-Bernoulli Beam Models

In this thesis, we consider control and dynamical behaviour of flexible beam models which have potential applications in robotic arms, satellite panel arrays and wind turbine blades. We study mathematical models that include flexible beams described by Euler-Bernoulli beam equations. These models consist of partial differential equations or combination of partial and ordinary differential equations depending on the loads and supports in the model. Our goal is to influence the models by control inputs such as external applied forces so that measured deflection profiles of the beams in the models behave as desired. We propose dynamic controllers for the output regulation, where the measurements from the models track desired reference signals in the given time, of flexible beam models. The controller designs are based on the so-called internal model principle and they utilize difference between measurement and desired reference trajectory. Moreover, the controllers are robust in the sense that they can achieve output regulation despite external disturbances and model uncertainties. We also study the output regulation problem when there are certain limitations on the control input. In particular, we generalize the theory of output regulation for dynamical systems described by ordinary differential equations subject to input constraints to a particular class of systems described by partial differential equations. We present set of solvability conditions and a linear output feedback controller for the output regulation

Control in moving interfaces and deep learning

Tesis Doctoral inédita leída en la Universidad Autónoma de Madrid, Facultad de Ciencias, Departamento de Matemáticas. Fecha de Lectura: 14-05-2021This thesis has received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie grant agreement No.765579-ConFlex

Diffuse Optical Imaging with Ultrasound Priors and Deep Learning

Diffuse Optical Imaging (DOI) techniques are an ever growing field of research as they are noninvasive, compact, cost-effective and can furnish functional information about human tissues. Among others, they include techniques such as Tomography, which solves an inverse reconstruction problem in a tissue volume, and Mapping which only seeks to find values on a tissue surface. Limitations in reliability and resolution, due to the ill-posedness of the underlying inverse problems, have hindered the clinical uptake of this medical imaging modality. Multimodal imaging and Deep Learning present themselves as two promising solutions to further research in DOI. In relation to the first idea, we implement and assess here a set of methods for SOLUS, a combined Ultrasound (US) and Diffuse Optical Tomography (DOT) probe for breast cancer diagnosis. An ad hoc morphological prior is extracted from US B-mode images and utilised for the regularisation of the inverse problem in DOT. Combination of the latter in reconstruction with a linearised forward model for DOT is assessed on specifically designed dual phantoms. The same reconstruction approach with the incorporation of a spectral model has been assessed on meat phantoms for reconstruction of functional properties. A simulation study with realistic digital phantoms is presented for an assessment of a non-linear model in reconstruction for the quantification of optical properties of breast lesions. A set of machine learning tools is presented for diagnosis breast lesions based on the reconstructed optical properties. A preliminary clinical study with the SOLUS probe is presented. Finally, a specifically designed deep learning architecture for diffusion is applied to mapping on the brain cortex or Diffuse Optical Cortical Mapping (DOCM). An assessment of its performances is presented on simulated and experimental data